Question

In what ratio does the x-axis divide the line segment joining the points (2, –3) and (5, 6)? Also, find the coordinates of the point of intersection.
[3 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark
Answer: 1 Mark

Let the required ratio be $\lambda :1$. Then, the coordinates of the point of division are,

$R\left(\frac{5\lambda +2}{\lambda +1},\frac{6\lambda -3}{\lambda +1}\right)$

But, it is a point on x-axis on which y-coordinates of every point is zero.

$\therefore \frac{6\lambda -3}{\lambda +1}=0\Rightarrow \lambda =\frac{1}{2}$

Thus, the required ratio is $\frac{1}{2}:1$ or 1:2.

Substituting $\lambda =\frac{1}{2}$ in the coordinates of R.

$R\left(\frac{5\lambda +2}{\lambda +1},0\right)$

$\Rightarrow R\left(\frac{\frac{5}{2}+2}{\frac{1}{2}+1},0\right)$

$\Rightarrow R(\frac{\frac{9}{2}}{\frac{3}{2}},0)$

$\Rightarrow R(3,0)$

$\therefore$ the coordinates of R are (3, 0)